Chemistry 231. Physical Transformations of Pure Substances. The Definition of a Phase. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties. Three Principal kinds of phases Solid – long-range order Liquid – less long-range order
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Physical Transformations of Pure Substances
For two phases to be in equilibrium, the chemical potential of the substance in both phases must be equivalent.
F = 3-2 = 1
The pressure of the vapour above the liquid is called the vapour pressure PJ.
Vapour pressures are temperature dependent.
Assume we apply an infinitesimal change in T or P to two phases in equilibrium
When a pressure (or temperature) change is applied to an equilibrium system of two phases (point a), the equilibrium is disturbed.
It can be restored by changing the temperature (or pressure) along the boundary to point b.
Defining the transition
The slope of any phase boundary can be obtained from the Clapeyron equation
For the fusion transition
We can re-write the Clapeyron equation to include the enthalpy of fusion
The dependence of the melting point on the applied pressure is given as follows
From the Clapeyron equation, a typical solid-liquid phase boundary slopes steeply upwards.
Most substances increase their melting points behave in this way.
For the transition between a condensed phase and the vapour phase
We can re-write the Clapeyron equation to include the enthalpy of the transition
Using the ideal gas equation
Note – tr represents vapourization
Critical temperature (Tc) - the temperature above whicha gas cannot be liquefied
Critical pressure (Pc) – the minimum pressure that needs to be applied at Tc to bring about liquefaction.
Supercritical fluid – fluid at or above the Tc value.
The phase boundary from the plot of the (T,P) equilibrium points.
The liquid vapour phase boundary terminates at the critical point (not shown).
The solid-vapour phase boundary is identical in shape.
The temperature dependence of the phase stability is related to the numerical value of the molar entropy!
The dependence of the chemical potential with pressure depends on the volume of the phase!
When we classify phase transitions, we must look at the first and second derivatives of the chemical potentials
The changes in thermodynamic properties for a schematic first-order transition.
The changes in thermodynamic properties for a schematic second-order transition.
The fluid-superfluid transition in helium (the transition).
The heat capacity appears to become infinite (first order).
It actually rises smoothly at the transition point, instead of exhibiting a singularity.
(P,T) regions where the phases are thermodynamically stable.
A phase boundary is a curve in (T,P) space where the values of the substance in the different phases are equivalent.
An invariant point where the solid, liquid, and vapour phases are in mutual equilibrium.